Math Problem Solver

\[ \frac{4}{9} + \frac{3}{4} - \frac{3}{4} + \frac{9}{4} - 2 = \frac{25}{36} = 0.69\overline{4} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{4}{9}\), \(\frac{3}{4}\), \(\frac{-3}{4}\), \(\frac{9}{4}\), and \(\frac{-2}{1}\) is \(36\). \[ \begin{aligned} \frac{4}{9} + \frac{3}{4} - \frac{3}{4} + \frac{9}{4} - 2 &= \frac{4 \cdot 4}{9 \cdot 4} + \frac{3 \cdot 9}{4 \cdot 9} + \frac{-3 \cdot 9}{4 \cdot 9} + \frac{9 \cdot 9}{4 \cdot 9} + \frac{-2 \cdot 36}{1 \cdot 36} \\ &= \frac{16 + 27 + -27 + 81 + -72}{36} \\ &= \frac{25}{36} \end{aligned} \]